Let's say I've found a crossbow which has a bonus to enemy dodge chance reduction. Will that help me with my melee attacks? And let's say I have the axe skill and am duel-wielding a pair of axes. Will my increased critical chance also affect my ranged attacks?

With version 1.0.6 and prior (not sure how much further, but it is not the case with 1.0.9), damage bonuses applied to both types of attacks - a fire damage bonus on a bow would also apply to melee combat.
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MichaelTDec 26 '11 at 20:14

I remember that several buffs are specifical to a weapon type. Enchantments over weapons, for what i know, are valid as long as you have that weapon equipped and if it's not specified otherwise, they always work.